Question

(1/а^2-ав -3в^2/а^4-ав^3 -в/а^3+а^2в+ав^2)*(в+а^2/а+в)

Answer 1

$1)\frac{1}{a^{2}-ab} -\frac{3b^{2}}{a^{4}-ab^{3}} -\frac{b}{a^{3}+a^{2}b+ab^{2}}=\frac{1}{a(a-b)}-\frac{3b^{2}}{a(a^{3}-b^{3})}-\frac{b}{a(a^{2}+ab+b^{2})}=\frac{1}{a(a-b)}-\frac{3b^{2}}{a(a-b)(a^{2}+ab+b^{2})}-\frac{b}{a(a^{2}+ab+b^{2})}=\frac{a^{2}+ab+b^{2}-3b^{2}-ab+b^{2}}{a(a-b)(a^{2}+ab+b^{2})} =\frac{a^{2}-b^{2}}{a(a-b)(a^{2}+ab+b^{2})}= \frac{a+b}{a(a^{2}+ab+b^{2})}$

$2)\frac{a+b}{a(a^{2}+ab+b^{2})}*(b+\frac{a^{2}}{a+b})=\frac{a+b}{a(a^{2}+ab+b^{2})} *\frac{ab+b^{2}+a^{2}}{a+b}=\frac{1}{a}$